Prime Numbers and Factors Worksheet for Olympiad

Maths Olympiad topic 31: Primes and divisors · Set 206 · 40 questions

How to solve it (Factors come in pairs): Find factors in pairs: 1 × N, 2 × …, 3 × …, until the pairs meet. Prime factorisation: keep dividing by the smallest prime that works, then group equal primes as powers. 1 is not a prime; 2 is the only even prime. To test a number, try dividing by the primes up to its square root.

1. 1.How many factors does 63 have? (a) 4 (b) 7 (c) 6 (d) 5
2. 2.What is the smallest prime factor of 91? (a) 1 (b) 7 (c) 13 (d) 2
3. 3.How many prime numbers are there between 50 and 60? (a) 4 (b) 1 (c) 3 (d) 2
4. 4.What is the prime factorisation of 140? (a) 2 × 5 × 7² (b) 2 × 5 × 7 (c) 2³ × 5 × 7 (d) 2² × 5 × 7
5. 5.How many prime numbers are there between 40 and 50? (a) 4 (b) 5 (c) 3 (d) 2
6. 6.What is the prime factorisation of 112? (a) 2 × 7⁴ (b) 2⁴ × 7 (c) 2³ × 7 (d) 2⁵ × 7
7. 7.What is the prime factorisation of 560? (a) 2⁴ × 5 × 7 (b) 2 × 5 × 7⁴ (c) 2³ × 5 × 7 (d) 2⁵ × 5 × 7
8. 8.What is the smallest prime factor of 133? (a) 19 (b) 1 (c) 2 (d) 7
9. 9.What is the smallest prime factor of 145? (a) 5 (b) 29 (c) 2 (d) 1
10. 10.What is the prime factorisation of 80? (a) 2 × 5⁴ (b) 2³ × 5 (c) 2⁵ × 5 (d) 2⁴ × 5
11. 11.How many prime numbers are there between 90 and 100? (a) 0 (b) 3 (c) 2 (d) 1
12. 12.How many prime numbers are there between 60 and 80? (a) 5 (b) 7 (c) 4 (d) 6
13. 13.How many prime numbers are there between 20 and 40? (a) 6 (b) 3 (c) 4 (d) 5
14. 14.What is the smallest prime factor of 21? (a) 7 (b) 1 (c) 3 (d) 2
15. 15.How many factors does 26 have? (a) 5 (b) 3 (c) 4 (d) 2
16. 16.What is the prime factorisation of 48? (a) 2 × 3⁴ (b) 2⁵ × 3 (c) 2³ × 3 (d) 2⁴ × 3
17. 17.What is the smallest prime factor of 77? (a) 1 (b) 11 (c) 7 (d) 2
18. 18.What is the smallest prime factor of 39? (a) 13 (b) 3 (c) 1 (d) 2
19. 19.What is the prime factorisation of 42? (a) 2 × 3 × 7 (b) 2² × 3 × 7 (c) 2³ × 3 × 7 (d) 2 × 3 × 7²
20. 20.How many factors does 91 have? (a) 4 (b) 5 (c) 3 (d) 2
21. 21.What is the prime factorisation of 360? (a) 2³ × 3² × 5 (b) 2 × 3² × 5³ (c) 2² × 3² × 5 (d) 2⁴ × 3² × 5
22. 22.How many prime numbers are there between 70 and 90? (a) 7 (b) 6 (c) 5 (d) 4
23. 23.What is the prime factorisation of 210? (a) 2² × 3 × 5 × 7 (b) 2³ × 3 × 5 × 7 (c) 2 × 3 × 5 × 7 (d) 2 × 3 × 5 × 7²
24. 24.How many prime numbers are there between 30 and 50? (a) 5 (b) 7 (c) 6 (d) 4
25. 25.What is the smallest prime factor of 169? (a) 3 (b) 1 (c) 2 (d) 13
26. 26.How many factors does 87 have? (a) 5 (b) 4 (c) 3 (d) 2
27. 27.What is the prime factorisation of 24? (a) 2⁴ × 3 (b) 2² × 3 (c) 2 × 3³ (d) 2³ × 3
28. 28.What is the prime factorisation of 60? (a) 2 × 3 × 5² (b) 2³ × 3 × 5 (c) 2² × 3 × 5 (d) 2 × 3 × 5
29. 29.How many factors does 28 have? (a) 4 (b) 5 (c) 7 (d) 6
30. 30.What is the prime factorisation of 504? (a) 2 × 3² × 7³ (b) 2³ × 3² × 7 (c) 2² × 3² × 7 (d) 2⁴ × 3² × 7
31. 31.How many prime numbers are there between 90 and 120? (a) 8 (b) 6 (c) 5 (d) 7
32. 32.How many factors does 104 have? (a) 6 (b) 9 (c) 8 (d) 7
33. 33.How many prime numbers are there between 30 and 60? (a) 8 (b) 9 (c) 6 (d) 7
34. 34.What is the prime factorisation of 15? (a) 3 × 5 (b) 3³ × 5 (c) 3² × 5 (d) 3 × 5²
35. 35.What is the smallest prime factor of 69? (a) 3 (b) 1 (c) 23 (d) 2
36. 36.How many prime numbers are there between 20 and 30? (a) 4 (b) 2 (c) 3 (d) 1
37. 37.What is the smallest prime factor of 217? (a) 2 (b) 31 (c) 1 (d) 7
38. 38.How many factors does 72 have? (a) 10 (b) 12 (c) 11 (d) 13
39. 39.How many factors does 33 have? (a) 2 (b) 3 (c) 5 (d) 4
40. 40.How many factors does 120 have? (a) 17 (b) 15 (c) 14 (d) 16

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